The main object of this paper is to present a systematic introduction to the theory and applications of the extended Appell-Lauricella hypergeometric functions defined by means of the extended beta function and extended Dirichlet's beta integral. Their connections with the Laguerre polynomials, the ordinary Lauricella functions and the Srivastava-Daoust generalized Lauricella functions are established for some specific paramters. Furthermore, by applying the various methods and known formulas

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... uch as fractional integral technique; some results of the Lagrange polynomials), we also derive some elegant generating functions for these new functions.